A small shop located in Utica sells a variety of dried fruits and nuts. The shop caters to travelers of all types;
it sells one-pound boxes of individual items, such as dried bananas, as well as two kinds of one-pound boxes of mixed fruits and nuts, called “Trail Mix” and “Subway Mix”. Because of the health inspection issues, individual items and mixed items can only be sold as packaged one-pound boxes. Here are the amounts of current supplies: Item Dried Bananas 800 pounds Dried Apricots 600 pounds Coconut Pieces 500 pounds Raisins 700 pounds Walnuts 1200 pounds The selling prices of the various types of boxes offered are: Trail Mix $9 per box Subway Mix $12 per box Dried Bananas $5 per box Dried Apricots $8 per box Coconut Pieces $10 per box Raisins $6 per box Walnuts $15 per box The manager would like to obtain as much revenue as possible from selling these boxed products. The management also decided that no more than 70% but at least 30% of these boxed products should be allocated to the Mixes. The Trail Mix consists of equal parts of all individual items, whereas the Subway Mix consist of 2 parts of walnuts and one part each of dried bananas, raisins, and coconut pieces. There are no dried apricots in the Subway Mix. a.)Formulate and list the linear program for this problem. Report your production decision and its dereived revenue.
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